Image-forming MR methods which utilize the interaction between magnetic fields and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for the imaging of soft tissue they are superior to other imaging methods in many respects, do not require ionizing radiation and are usually not invasive.
According to the MR method in general, the body of the patient to be examined is arranged in a strong, uniform magnetic field (B0 field) whose direction at the same time defines an axis (normally the z-axis) of the co-ordinate system on which the measurement is based. The magnetic field produces different energy levels for the individual nuclear spins in dependence on the magnetic field strength which can be excited (spin resonance) by application of an electromagnetic alternating field (RF field, also referred to as B1 field) of defined frequency (so-called Larmor frequency, or MR frequency). From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate frequency (RF pulse), so that the magnetization performs a precessional motion about the z-axis. The precessional motion describes a surface of a cone whose angle of aperture is referred to as flip angle. The magnitude of the flip angle is dependent on the strength and the duration of the applied electromagnetic pulse. In the case of a so-called 90° pulse, the spins are deflected from the z axis to the transverse plane (flip angle 90°).
After termination of the RF pulse, the magnetization relaxes back to the original state of equilibrium, in which the magnetization in the z direction is built up again with a first time constant T1 (spin lattice or longitudinal relaxation time), and the magnetization in the direction perpendicular to the z direction relaxes with a second time constant T2 (spin-spin or transverse relaxation time). The variation of the magnetization can be detected by means of one or more receiving RF coils which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicular to the z-axis. The decay of the transverse magnetization is accompanied, after application of, for example, a 90° pulse, by a transition of the nuclear spins (induced by local magnetic field inhomogeneity) from an ordered state with the same phase to a state in which all phase angles are uniformly distributed (dephasing). The dephasing can be compensated by means of a refocusing pulse (for example a 180° pulse). This produces an echo signal (spin echo) in the receiving coils.
In order to realize spatial resolution in the body, linear magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving coils then contains components of different frequencies which can be associated with different locations in the body. The MR signal data obtained via the RF coils corresponds to the spatial frequency domain and is called k-space data. The k-space data usually includes multiple lines acquired with different phase encoding. Each line is digitized by collecting a number of samples. A set of k-space data is converted to a MR image by means of Fourier transformation or other appropriate reconstruction algorithms.
MR imaging of tissues with very short transverse relaxation times, such as bone or lung, is becoming increasingly important. Nearly all known methods for this purpose basically employ three-dimensional (3D) radial k-space sampling. In the so-called zero echo time (ZTE) technique a readout gradient is set before excitation of magnetic resonance with a high-bandwidth and thus short, hard RF pulse. In this way, gradient encoding starts instantaneously upon excitation of magnetic resonance. The acquisition of a free induction decay (FID) signal starts immediately after radiation of the RF pulse resulting in an effectively zero ‘echo time’ (TE). After the FID readout, only minimal time is required for setting of the next readout gradient before the next RF pulse can be applied, thus enabling very short repetition times (TR). The readout direction is incrementally varied from repetition to repetition until a spherical volume in k-space is sampled to the required extent. Without the need for switching off the readout gradient between TR intervals, ZTE imaging can be performed virtually silently (see Weiger et al, Magnetic Resonance in Medicine, vol. 70, p. 328-332, 2013).
A challenge in ZTE imaging is that the k-space data are slightly incomplete in the k-space center due to the initial dead time that is caused by the finite duration of the RF pulse, transmit-receive switching, and signal filtering.
This k-space gap can be addressed, for example, by combining the radial ZTE sampling with extra Cartesian sampling of the k-space center, like in the known PETRA technique (see Grodzki et al, Magnetic Resonance in Medicine, vol. 67, p. 510-518, 2012). However, a drawback of the PETRA approach is that the imaging is no longer silent due to the necessary gradient switching for the Cartesian acquisition of the k-space center.